An author gains the interest of a reader with what's known as a "hook." The hook is usually something interesting, like a startling fact or a poignant quote. For example, the opening line of Fahrenheit 451 by Ray Bradbury is, "It was a pleasure to burn."
This hook is interesting because it can get the reader thinking a few different things: What is being burned? Who is doing the burning? Why is it pleasurable? The next line draws the reader in even further: "It was a special pleasure to see things eaten, to see things blackened and changed." Now the reader is getting a better idea as to what is being burned and why it's pleasurable to the person doing the burning.
As far as hooks go; however, it depends on the type of literature in which it's being used. Authors can gain the interest of readers for multiple reasons in different ways. In the interest of entertainment, though, a hook will often intrigue the reader and draw them in to wanting to know more. In essence, "hooking" the reader!